Joint localization of directed polymers

Yuri Bakhtin, Douglas Dow

Research output: Contribution to journalArticlepeer-review


We consider (1 + 1)-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started at different starting points, all the associated endpoint distributions localize in a common random region that does not grow with the length of the polymer. In particular, we prove that joint localization holds when the reference random walk of the polymer model is either a simple symmetric lattice walk or a Gaussian random walk. We also prove that the very strong disorder property holds for a large class of space-continuous polymer models, implying the usual single polymer localization.

Original languageEnglish (US)
Article number109
JournalElectronic Journal of Probability
StatePublished - 2023


  • directed polymers
  • joint localization
  • localization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Joint localization of directed polymers'. Together they form a unique fingerprint.

Cite this